A physics student wants to make sense of the various symbols used to represent "approximately equal to" -- as well as the phrase's mathematical meaning. Doctor Vogler produces two precise definitions while acknowledging that context, and personal preference, rule the day.

As I read various algebra books for high school kids, I find what
appears to be an inconsistent use of the words 'quadratic equation',
and I wanted to be sure I use it correctly myself. Is it correct to
call y = ax^2 + bx + c a 'quadratic equation', or a 'quadratic function'?

A teacher's textbook, and his colleagues, all assume that if two geometric objects have
different tick marks, then the two angles or segments indicated must be incongruent.
Doctor Peterson unpacks the ambiguity, then warns against the larger error of reading
too much in sketches.

A line is 1 dimensional, a square or rectangle is 2 dimensional, and a
cube is 3 dimensional. My question is what if you throw in parabolas
or circles or the absolute value function, etc.? A circle is kind of
like a parabola, but it is very much like a square, so I am thinking
it is 2-dimensional. My conclusion is that the only 1 dimensional
object is a straight line, and a point is 0 dimensional, but I am not
confident that I am correct. Can you please clear this up for me?

A student wonders whether the labels "undefined" and "indeterminate form" could
apply to one and the same expression. Doctor Vogler considers several expressions,
functions, and limits to distinguish the different contexts that call for such terminology.